Steve Smith put in a captain's performance as Rajasthan Royals claimed a seven-wicket victory over Mumbai Indians in the Indian Premier League on Tuesday.

The Australia international's unbeaten 79 was instrumental in the Royals' chase of a 165-run target, which was achieved with five balls to spare.

Smith, though, will have been as concerned as anyone to see Australia Twenty20 captiain Aaron Finch assisted from the field after appearing to seriously injure his left hamstring in lunging for a quick single early in the Indians' innings.

Full details are yet to emerge, but the Indians - who remain without a win this season - and Australia will fear a lengthy spell on the sidelines for the opening batsman.

The Indians, hampered by that early injury to Finch (retired hurt on 10), were slow to get out of the blocks, losing Parthiv Patel and and Rohit Sharma for 16 and a duck respectively.

Unmukt Chand, who came in for Finch, could only muster 11, but Corey Anderson (50) and Kieron Pollard (70) helped fire the Indians to a defendable score of 164-5.

Anderson, then on 23, looked to have been dismissed with the final ball of the 15th over, but Dhawal Kulkarni's delivery was deemed illegal, allowing the New Zealander to remain at the crease until the innings was almost up.

The Royals' - buoyed by a 100 per cent record in the competition so far - went about their chase in assured fashion, with Sanju Samson (17) the first to fall when his side were 28-1.

Samson's dismissal signalled the arrival of Smith at the crease, and his 64-run partnership with Ajinkya Rahane (46) put the Royals on course to snare a third successive victory.

Deepak Hooda (13) and James Faulkner (6 not out) made late cameos, but it was Smith's 34-run haul from overs 17 to 19 that really delivered the win.

Faulkner survived a run-out appeal after grabbing a single with the first delivery of final over, bringing the curtain down on yet another Royals victory.